is there a modifier to slightly shrink/grow mesh so it doesn't overlap?
Well, what I always do is select the model, tap the S key, or whatever you may have for scale, and then type in (actual numbers) on how much bigger you want to scale it.
I think it works best when you go to the Object Properties by hitting N and finding the model's scale, then choose either to scale it in the X, Y or Z axis. If all axis' are the same size, just click the highest box and drag down to select them all, find the number and increase it by 0.5 or if you wanna be really precise 0.05, just keep adding to it until you get the desired result.